For \( k \in \mathbb {Z}_{\ge 0} \)  we have a denumerable sequence of \( K(s_k) \)  values and we know that \( K(s) \)  is bounded in the finite \(s\) -plane.
Clearly \( K(s) \)  is entire, and the question we pose is that of interpolation of an entire function, i.e. reconstructing it from this sequence of values on \(\mathbb {Z}_{\ge 0}\) .
This question was addressed in 1884 with the Mittag-Leffler theorem [1]}, [2]}, [3]}, [4]},
by the Pringsheim interpolation formula [5]}, and by Guichard's theorem [6]}.
However use of these involve restrictions which are not satisfied by \( K(s) \) .
